At first, you should take care that you are not have a category selected, click "All Content" to assure to get all content listed.
Assure that the display menu is not set to "On this device"
The player check for new content right when it gets started. In case the player was already started and running during the order, click "Update Content" from the top right menu.
There is no such a "logout". If you have decided, no longer use the player on your current device, you can select "Deauthorize this device" from the settings menu.
You do not need to download the Flux Player every time. You are opening the installer each time. You only need to install and sign in to the Flux Player once on your PC. After that, you should open the installed player app and not the installer app.
The player do not allow capturing the screen. All technics work that way, like screen mirroring from a mobile device will show a black screen. To play a video on a TV, use Apple Air play or a Chromecast.
There is a workaround for this problem. The app stop working because the Android battery optimization force to stop it. You can remove the app from the list of battery optimization, this will fix this behavior.
Here two links explaining how to do this:
https://www.techrepublic.com/article/how-to-remove-android-apps-from-the-battery-optimization-list/
The codes, only assign the content to your account. After redeeming the code, it becomes invalid. From then on, the content can accessed by sign in with email and password.